Question: Simplify the following expression: $ q = \dfrac{z + 1}{-2z - 9} + \dfrac{7}{4} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4}{4}$ $ \dfrac{z + 1}{-2z - 9} \times \dfrac{4}{4} = \dfrac{4z + 4}{-8z - 36} $ Multiply the second expression by $\dfrac{-2z - 9}{-2z - 9}$ $ \dfrac{7}{4} \times \dfrac{-2z - 9}{-2z - 9} = \dfrac{-14z - 63}{-8z - 36} $ Therefore $ q = \dfrac{4z + 4}{-8z - 36} + \dfrac{-14z - 63}{-8z - 36} $ Now the expressions have the same denominator we can simply add the numerators: $q = \dfrac{4z + 4 - 14z - 63}{-8z - 36} $ $q = \dfrac{-10z - 59}{-8z - 36}$ Simplify the expression by dividing the numerator and denominator by -1: $q = \dfrac{10z + 59}{8z + 36}$